Try temporarily disabling WiFi so your phone is just using mobile data (cellular) instead and see if that makes any difference. It could just be a matter where it doesn't matter which text messaging app you're using, it's the type of online connectivity that's in use.
MMS is a really dated protocol so it has limitations with today's technology. It's strong point being SMS and MMS are the only two protocols all the text messaging apps support, and the over-riding problem is text messaging has devolved into a toxic mess of competing, proprietary protocols that are isolated from each other. Since almost all of us are using either Android or iOS with different text messaging services and different carriers, when it involves text message exchanges it might involve two people using similar, corresponding parameters but the odds are the exchange will be between say, someone using an Android phone and WhatsApp on one end and an iPhone user and iMessage on the other end. Neither the WhatsApp protocol nor the iMessage protocol are compatible with each other so MMS, and all its limitations, is the fallback. In your case, it could just be a matter where some MMS exchanges work out better via cellular connectivity, not WiFi. That's not an app issue nor some setting you can change, that's a cellular carrier issue tied to that pissing match between the competing corporations.